Azimuthal metallicity variations, spiral structure, and the failure of radial actions based on assuming axisymmetry

ABSTRACT We study azimuthal variations in the mean stellar metallicity, $\langle {\rm{[Fe/H]}}\rangle $, in a self-consistent, isolated simulation in which all stars form out of gas. We find $\langle {\rm{[Fe/H]}}\rangle$ variations comparable to those observed in the Milky Way and which are coincident with the spiral density waves. The azimuthal variations are present in young and old stars and therefore are not a result of recently formed stars. Similar variations are present in the mean age and $\rm \alpha$-abundance. We measure the pattern speeds of the $\langle {\rm{[Fe/H]}}\rangle$-variations and find that they match those of the spirals, indicating that spirals are the cause of the metallicity patterns. Because younger stellar populations are not just more $\rm [Fe/H]$-rich and $\rm \alpha$-poor but also dynamically cooler, we expect them to more strongly support spirals, which is indeed the case in the simulation. However, if we measure the radial action, $J_{R}$, using the Stäckel axisymmetric approximation, we find that the spiral ridges are traced by regions of high $J_{R}$, contrary to expectations. Assuming that the passage of stars through the spirals leads to unphysical variations in the measured $J_{R}$, we obtain an improved estimate of $J_{R}$ by averaging over a $1\rm{\:{Gyr}}$ time interval. This time-averaged $J_{R}$ is a much better tracer of the spiral structure, with minima at the spiral ridges. We conclude that the errors incurred by the axisymmetric approximation introduce correlated deviations large enough to render the instantaneous radial actions inadequate for tracing spirals.